Analysis of the Vibration of the Ground Surface by Using the Layered Soil: Viscoelastic Euler Beam Model due to the Moving Load

Moving loads will have a certain impact on the safety of the structures. Since concrete is a viscoelastic material, the elastic concrete model cannot describe its viscoelastic characteristics under moving loads. It is necessary to establish a model that can describe the viscoelastic characteristics of concrete materials. In addition, the layered of the soil is also an important factor affecting the propagation of subway vibration waves. Considering the effects of the properties of the concrete material of the subway tunnel structure and the layered soil foundation as well as the load velocity on the vibration of the ground surface caused by the moving load, the standard linear elastic solid Euler beam model is described for the subway tunnel structure in this paper. The equivalent stiffness of the layered soil-viscoelastic beam coupling system subjected to a moving load is formed by using the transmission and reflection matrix (TRM) method. The numerical solution of ground surface displacement caused by subway tunnel in time-space domain is obtained by IFFT algorithm. The correctness of the algorithm is verified by comparing with the reference results. Numerical results show that, with the increase of the viscous coefficient of the viscoelastic Euler beam, the vibration amplitude of the ground surface will decrease. Up to a certain value of the increasing the viscous coefficient of the Euler beam, it will have little effect on the vibration amplitude of the ground surface. Therefore, the standard solid model of viscoelastic Euler beam can well describe the creep and relaxation of materials. The model of viscoelastic beam is reasonable for the working condition of subway tunnel concrete structure. At high speed of moving load, the maximum value of ground surface displacement spectrum will appear at the smaller frequency domain and the maximum value of displacement spectrum will also increase for the soft layer soil, while it is opposite to that of the stiffer layer soil.